You received a rejection message from Apple "We noticed that your app uses a third-party login service but does not offer Sign in with Apple". This article explains why this occurs and how you can work around it so Apple will approve your app.
Apple rejected your iOS App providing this 'Sign in with Apple' related message:
Guideline 4.8 - Design - Sign in with Apple
To resolve this issue, please revise your app to offer Sign in with Apple as an equivalent login option.
To learn more, see the Sign in with Apple Overview.
This shows that your iOS app has been rejected by Apple because of Guideline 4.8 - Design - Sign in with Apple.
Usually, along with the above rejection message from Apple, a screenshot is provided like the one below, which displays third-party or social login services without the Apple Sign in option.
On September 12, 2019, Apple added a new guideline to its App Store Review Guidelines, under Design, Guideline 4.8. Apple's new guideline requires all new apps, that use a third-party or social login service, as shown in the image above, offer Apple Sign-in as an equivalent service. As mentioned, existing apps should have complied by April 2020.
For further details have a look at:
Thus, Apple is not allowing authentication with third-party login services if sign in with Apple is not also included.
The BiznessApps team is working on a solution and now is in the process of releasing it.
Till then, you will not be able to use third-party login services. To this end, navigate on your app's Dashboard to Settings -> App Screens menu and disable these options.